3.2 Population assignment and structure
Pairwise Fst  comparisons between regional samples showed low to moderate values  ranging from 0.05 to 0.21; all comparisons were significant (Fig. S2, Supporting information). The highest Fst  value  was recovered between Guatemala and Australia, and lowest Fst  values were obtained comparing Spain and Greece (0.05) and their respective comparisons with Australia (0.08 and 0.09). South African specimens showed moderate Fst  values in pairwise comparisons with all sites, although slightly higher with the Spanish and Greek (0.18 in both cases) than with Neotropical and Australasian sampling sites.
DAPC detected an optimal genetic cluster of two ( = 2) followed by three (K  = 3) based on the AIC value (Fig. S3A, Supporting information). DAPC results for K=  2 identified two clusters (South Africa and Brazil) versus the rest, i.e. Spain, Greece, Guatemala and Australia (Fig. S4A, Supporting information). The DAPC results for  = 3, with 16 principal components explaining 46.7% of the variance, showed two separated clusters (South Africa and Brazil) and the rest (Fig. 2A). Group assignment analysis (compoplot  function) supported these clusters with a high probability of assignation (Fig. S4B, Supporting information). Unexpectedly, the assignment plot placed one individual from SA (SA_8) (Fig. S4B-C, supporting information) into the cluster composed of all other populations, indicating the ancestral presence of the colonising alleles in low frequency or potential back colonisation from the colonised areas.  Moreover, STRUCTURE analyses identified K =2 as the most probable number of genetic clusters followed by K =3, with some differences in the groupings as compared to the DAPC analyses (Fig. S3C, Supporting information). For K =2, one cluster grouped all sampling sites except South Africa, which showed some degree of introgression (<20%) from another genetic cluster (dark blue in Fig. 2 top). When considering K =3, Brazilian individuals showed a small proportion of cluster assignation to a cluster also present in the South African population (light blue in Fig. 2B bottom). Further DAPC and STRUCTURE analyses were conducted, excluding samples from South Africa (Fig. 3A-B) to explore the introduced range in more detail. DAPC detected an optimal genetic cluster of three (K = 3) (Fig. S3B, Supporting information) with Brazilian samples as the most divergent population and some differentiation between Spain-Guatemala versus Greece-Australia (Fig. 3A). STRUCTURE analyses for K =2 detected a genetic break between Brazil and the rest of populations; forK =3, apart from identifying Brazil as belonging to a different genetic cluster, all individuals from Guatemala were assigned to a distinct genetic cluster, and individuals from Greece and Australia were mostly assigned to a separate cluster (with the exception of two individuals from Greece), while most individuals from Spain had mixed association with the former two clusters in roughly similar proportions (Fig. 3B).
The co-ancestry matrix generated by fineRADstructure  (Fig. 4) showed that all individuals of the respective locations clustered together, with the exception of European samples from Spain and Greece, which appeared mixed in two different groups. The most distinct group of samples was South Africa, showing the highest values of co-ancestry, followed by Brazil. Both also showed higher ancestry relationships compared to the remaining sampling locations, i.e. they presented fewer allele differences among them compared to the remaining sampling sites. All other samples formed a cluster that could be subdivided into two subclusters: subcluster A, including Australia and a mix of samples from Spain and Greece; and subcluster B, including all samples from Guatemala and the remaining Spanish and Greek samples. The samples from Europe (Spain and Greece) showed strong evidence of heterogeneous gene flow (indistinguishable genetic ancestry).